Question

PLEASE HELP Ruby has a choice between three savings accounts. Savings account A has an APR of 3.9742% compounded monthly, savings account B has an APR of 3.9886% compounded quarterly, and savings account C has an APR of 3.9998% compounded semiannually. Ruby wants to choose the savings account with the highest APY.

Part I: If r is a savings account's APR and n is the number of compounding periods per year, what expression gives the savings account's APY?
Part II: What is the APY of savings account A to four decimal places?
Part III: What is the APY of savings account B to four decimal places?
Part IV: What is the APY of savings account C to four decimal places?
Part V: Which savings account offers the highest APY?

Answer 1

I. APY = (1 +r/n)^n -1

II. 4.0474%

III. 4.0487%

IV. 4.0398%

V. Account B

Explanation:

I. The expression is ...

APY = (1 +r/n)^n -1

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II–IV. See the attached. (When calculations are tedious and repetitive, a spreadsheet is helpful.)

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V. The account compounded quarterly has the highest APY, account B.